An elliptical Gaussian wave formalism model of a charged-particle beam is proposed by analogy with an elliptical Gaussian light beam.In the paraxial approximation.the charged-particle beam can be described as a whole by a complex radius of curvature in the real space domains.Therefore,the propagation and transform of charged-particle beam passing through a first-order optical system is represented by the ABCD-like law.As an example of the application of this model,the relation between the beam waist and the minimum beam spot at a fixed target is discussed.The result.well matches that from conventional phase space model,and proves that the Gaussian wave formalism model is highly effective and reasonable.